Upon further investigation, it appears it was just a single trophy, as I noticed it would crash me out even just trying to look at it, it wouldn't load the slot, and then the instance would kick/drop/crash me. I decided to hit it with a removal tool after I realized it was just this one.
This returned to me the blank trophy plus dropped a Player Name +1 head bag. I had only put in one stag head to begin with I think.
I then decided to attempt to use my good stag head to make a new trophy on a different wall, and it worked fine. I then decided to hit it with a removal hammer just to see what happens, and it just returns the blank trophy to my inventory without a head.
I'm not sure if it's related, but last night I noticed that all my shared containers and workbenches and stuff had been unshared, and others (like Razzberry's community center) had also been unshared. I suspect perhaps there was a weird server hiccup or something, but I obviously have no way to confirm this.
I'm not sure if this makes this bug solved or not. The heads still appear to not work correctly when stacked, is it possible to make them a type of thing that doesn't stack in inventory perhaps so they can't accidentally stack I wonder?